Question: In terms of $\pi$, what is the area of the circle defined by the equation $2x^2+2y^2+10x-6y-18=0$?
Answer: Dividing by 2, we get
\[x^2 + y^2 + 5x - 3y - 9 = 0.\]Completing the square in $x$ and $y,$ we get
\[\left( x + \frac{5}{2} \right)^2 + \left( y - \frac{3}{2} \right)^2 = \frac{35}{2},\]so the area of the circle is $\boxed{\frac{35}{2} \pi}.$